Mathematics, 20.07.2019 01:20 shels10tay
Let a elementof m_n(r) be a diagonalizable matrix with tr(a^2) = 0. prove that a is the zero matrix.
Answers: 1
(R) be a diagonalizable matrix with 
given ![\left[\begin{array} {ccc}a_{11}&0&0\\0&a_{22}&0\\0&0&a_{33}\end{array}\right]](/tpl/images/0109/8845/ef7d8.png)
 be any  matrix of order
![A\times A=A^2=\left[\begin{array}{ccc}a_{11}&0&0\\0&a_{22}&0\\0&0&a_{33}\end{array}\right]\times \left[\begin{array}{ccc}a_{11}&0&0\\0&a_{22}&0\\0&0&a_{33}\end{array}\right]](/tpl/images/0109/8845/0800f.png)
![A^2=\left[\begin{array} {ccc}a^2_{11}&0&0\\0&a^2_{22}&0\\0&0&a^2_{33}\end{array}\right]](/tpl/images/0109/8845/de01a.png)
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Let a elementof m_n(r) be a diagonalizable matrix with tr(a^2) = 0. prove that a is the zero matrix....
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